The Reader provided only sketchy details.  I am not sure he is trying to design a boil-off tube as a part of process cooling or want to know the rate of boil-off steam in an existing set-up.  I guess the latter.

 

As I understand, he wants to know how much steam will be discharged from the mild steel pipe, assuming he will supply enough water to the pipe section to maintain the boil-off condition.  He should measure at least the pressure of boil-off steam inside the constricted tube section.  Since the tube is constricted at the upper end, its inside pressure would increase above atmosphere due to boil-off.  Once he finds the steam pressure inside the tube, he can use the Napier’s formula, if the boil-off steam is discharged to atmosphere.

 

Steam discharge through an orifice can be calculated using the Napier’s formula.